Documentation on the mathematical models used by Blender physics engines
Rigid bodies

There is no mention of the underlying physics engine in the manual for the current version v2.81.

However, up until version 2.79, Blender used to have also a Game Engine, which shared the same physics with the general Rigid Body World used for animation. Its manual gave more away in terms of the underlying engine:


  Blender includes advanced physics simulation in the form of the Bullet Physics Engine (Bullet Physics). Most of your work will involve setting the right properties on the objects in your scene, then you can sit back and let the engine take over.


As far as I can tell, Blender still uses Bullet. Unfortunately, the Bullet documentation doesn't explain things from the first principles up: it rather explains the settings, API and examples.

Liquids

The current (up to Blender 2.81) fluid engine is based on Lattice Boltzmann (LBM) through the elbeem library.

However, it is being replaced (version 2.82) by a new fluid engine, Mantaflow.